Geodesic
CLT for linear spectral statistics of Hermitian Wigner matrices with general moment conditions
Teoriâ veroâtnostej i ee primeneniâ, Tome 60 (2015) no. 2, pp. 311-332 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{TVP_2015_60_2_a5,
     author = {Z. Bao and J. Xie},
     title = {CLT for linear spectral statistics of {Hermitian} {Wigner} matrices with general moment conditions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {311--332},
     year = {2015},
     volume = {60},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2015_60_2_a5/}
}
TY  - JOUR
AU  - Z. Bao
AU  - J. Xie
TI  - CLT for linear spectral statistics of Hermitian Wigner matrices with general moment conditions
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2015
SP  - 311
EP  - 332
VL  - 60
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TVP_2015_60_2_a5/
LA  - en
ID  - TVP_2015_60_2_a5
ER  - 
%0 Journal Article
%A Z. Bao
%A J. Xie
%T CLT for linear spectral statistics of Hermitian Wigner matrices with general moment conditions
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2015
%P 311-332
%V 60
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_2015_60_2_a5/
%G en
%F TVP_2015_60_2_a5
Z. Bao; J. Xie. CLT for linear spectral statistics of Hermitian Wigner matrices with general moment conditions. Teoriâ veroâtnostej i ee primeneniâ, Tome 60 (2015) no. 2, pp. 311-332. http://geodesic.mathdoc.fr/item/TVP_2015_60_2_a5/

[1] Anderson G. W., Zeitouni O., “A CLT for a band matrix model”, Probab. Theory Related Fields, 134:2 (2006), 283–338 | DOI | MR | Zbl

[2] Bai Z. D., Silverstein J. W., Spectral Analysis of Large Dimensional Random Matrices, Science Press, Beijing, 2006, 393 pp. | Zbl

[3] Bai Z. D., Wang X. Y., Zhou W., “CLT for linear spectral statistics of Wigner matrices”, Electron. J. Probab., 14:83 (2009), 2391–2417 | MR | Zbl

[4] Bai Z. D., Yao J. F., “On the convergence of the spectral empirical process of Wigner matrices”, Bernoulli, 11:6 (2005), 1059–1092 | DOI | MR | Zbl

[5] Bai Z. D., Yin Y. Q., “Necessary and sufficient conditions for almost sure convergence of the largest eigenvalues of a Wigner matrix”, Ann. Probab., 16:4 (1988), 1729–1741 | DOI | MR | Zbl

[6] Diaconis P., Evans S. N., “Linear functionals of eigenvalues of random matrices”, Trans. Amer. Math. Soc., 353:7 (2001), 2615–2633 | DOI | MR | Zbl

[7] Guhr T., Müller-Groeling A., Weidenmüller H. A., “Random-matrix theories in quantum physics: common concepts”, Phys. Rep., 299:4–6 (1998), 189–425 | DOI | MR

[8] Johansson K., “On fluctuations of eigenvalues of random Hermitian matrices”, Duke Math. J., 91:1 (1998), 151–204 | DOI | MR | Zbl

[9] Jonsson D., “Some limit theorems for the eigenvalues of a sample covariance matrix”, J. Multivariate Anal., 12 (1982), 1–38 | DOI | MR | Zbl

[10] Marchenko V. A., Pastur L. A., “Raspredelenie sobstvennykh znachenii v nekotorykh ansamblyakh sluchainykh matrits”, Matem. sb., 72:4 (1967), 507–536 | MR | Zbl

[11] Mehta M. L., Random matrices, Elsevier, Amsterdam, 2004, 688 pp. | MR | Zbl

[12] Shcherbina M., “Central limit theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices”, J. Math. Phys. Anal. Geo., 7:2 (2011), 176–192 | MR | Zbl

[13] Sinaǐ Y. A., Soshnikov A., “Central limit theorem for traces of large random symmetric matrices with independent entries”, Bull. Braz. Math. Soc., 29:1 (1998), 1–24 | DOI | MR | Zbl

[14] Pan G. M., Zhou W., “Central limit theorem for signal-to-interference ratio of reduced rank linear receiver”, Ann. Appl. Probab., 18:3 (2008), 1232–1270 | DOI | MR | Zbl

[15] Pandey A., Mehta M. L., “Gaussian ensembles of random Hermitian matrices intermediate between orthogonal and unitary ones”, Comm. Math. Phys., 87:4 (1983), 449–468 | DOI | MR | Zbl

[16] Lytova A., Pastur L. A., “Central limit theorem for linear eigenvalues statistics of random matrices with independent entries”, Ann. Probab., 37:5 (2009), 1778–1840 | DOI | MR | Zbl